Join expressions of equal value$ 3(y+b)+4x $$ (3+4x)(y+b) $$ (4y+3)(x+b) $a.$ 3y+3b+4x $b.$ 4yx+4yb+3x+3b $c.$ 3y+3b+4xy+4xb $

1-No suitable expression, 2-c, 3-b

Match Equivalent Expressions: 3(y+b)+4x and Related Forms

Q: How do I know which terms to multiply together?

Use the distributive property: multiply the term outside parentheses by each term inside. For $ (3+4x)(y+b) $, multiply 3 by both y and b, then 4x by both y and b.

Q: What if I get confused with all the variables?

Take it one step at a time! First expand completely, then organize by grouping like terms together. Use different colors for x-terms, y-terms, and constants if it helps.

Q: How do I check if my expansion is correct?

Count your terms! The expanded form should have the same number of terms as the original multiplication would create. For $ (a+b)(c+d) $, you should get exactly 4 terms.

Q: Can I rearrange the terms in my final answer?

Yes! Addition is commutative, so $ 3y+3b+4x $ equals $ 4x+3y+3b $. Just make sure you don't change any coefficients or variables.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Open parentheses

00:04 Open parentheses properly, multiply by each factor

00:10 And this is the simplification to 1, let's continue to 2

00:16 Open parentheses properly, multiply each factor by each factor

00:20 Calculate the products

00:25 And this is the simplification to 2, let's continue to 3

00:28 Open parentheses properly, multiply each factor by each factor

00:33 Calculate the products

00:36 Calculate the products

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Join expressions of equal value

$3(y+b)+4x$
$(3+4x)(y+b)$
$(4y+3)(x+b)$
a. $3y+3b+4x$
b. $4yx+4yb+3x+3b$
c. $3y+3b+4xy+4xb$

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Expand each of the given expressions using the distributive property.
Step 2: Simplify the resulting expressions.
Step 3: Match the simplified expressions with options a, b, and c.

Now, let's work through each step:
Step 1: Start with the first expression $3(y+b) + 4x$ .
Applying the distributive property: $3 \cdot y + 3 \cdot b + 4x = 3y + 3b + 4x$ . This matches with option a: $3y+3b+4x$ .

Step 2: Consider the second expression $(3+4x)(y+b)$ .
Expanding using the distributive property, we get: $3(y+b) + 4x(y+b) = 3y + 3b + 4xy + 4xb$ . This matches with option c: $3y+3b+4xy+4xb$ .

Step 3: Finally, expand the third expression $(4y+3)(x+b)$ .
Apply the distributive property: $4y(x+b) + 3(x+b) = 4yx + 4yb + 3x + 3b$ . This matches with option b: $4yx+4yb+3x+3b$ .

Therefore, the matches are:
First expression matches option a
Second expression matches option c
Third expression matches option b

Therefore, the solution to the problem is 1-a, 2-c, 3-b.

3

Final Answer

1-a, 2-c, 3-b

Key Points to Remember

Essential concepts to master this topic

Distributive Property: Multiply each term inside parentheses by the outside factor
Technique: For $(3+4x)(y+b)$ , distribute: 3(y+b) + 4x(y+b)
Check: Verify by comparing terms: same variables and coefficients must match ✓

Common Mistakes

Avoid these frequent errors

Forgetting to distribute to all terms
Don't multiply only the first term in parentheses = missing terms in final answer! This gives incomplete expressions that won't match. Always distribute the outside factor to every single term inside the parentheses.

Practice Quiz

Test your knowledge with interactive questions

$(3+20)\times(12+4)=$

FAQ

Everything you need to know about this question

How do I know which terms to multiply together?

+

Use the distributive property: multiply the term outside parentheses by each term inside. For $(3+4x)(y+b)$ , multiply 3 by both y and b, then 4x by both y and b.

Why don't all the expressions look the same after expanding?

+

Even equivalent expressions can look different! Terms can be written in different orders (like 3y+4x vs 4x+3y) but still be equal. Focus on matching the same terms with same coefficients.

What if I get confused with all the variables?

+

Take it one step at a time! First expand completely, then organize by grouping like terms together. Use different colors for x-terms, y-terms, and constants if it helps.

How do I check if my expansion is correct?

+

Count your terms! The expanded form should have the same number of terms as the original multiplication would create. For $(a+b)(c+d)$ , you should get exactly 4 terms.

Can I rearrange the terms in my final answer?

+

Yes! Addition is commutative, so $3y+3b+4x$ equals $4x+3y+3b$ . Just make sure you don't change any coefficients or variables.

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